how much do the rounds actually matter

What does it mean if you speak with multiple people (like switching) vs. more than one person at a time vs. only one person the whole time?

It just means that's how a certain house is running that party that day with you there. There is no code to break or meaning for you to decipher, and there's nothing you can do about it either but have great conversations with everyone. There are advantages to meeting multiple people; more chances for you to impress and have a whole group knowing you and pulling for you instead of falling through the cracks. This is how most rounds will go. If you are talking to more than one at a time it could mean that the additional person is a floater and doesn't have an assigned place among the conversation groups, so she's either talking to you on purpose out of interest (maybe she's on recruitment team and making a point of checking you out), or maybe the conversation was not going well and she has stepped in to help. If you talk with one person the whole time it is likely to happen in later rounds and that person's job is to connect with you to ascertain your true interest in her sorority and/or to try to convince you that they really like you. Or maybe she's only babysitting you because they don't really care one way or the other about you at that point. Who can tell? Each party is a chance to make it to the next step. You are being way too analytical. Maybe you're writing a book?

Don't do that. You can't gauge interest by the mechanics of who talks to you, what room you're in, how you were walked out, none of that. It will drive you crazy and stress you out and you won't rush well. You are going to be disappointed and surprised at some point. Accept it and the fact that you can't predict or avoid it.